
Test the cold nature of DM particles. Cosmological
simulations of cold DM indicate that galaxy halos are full of
subhalos[1]}. Extrapolating the observed trends of
\(M_{\rm dyn}/L\)  vs. \(L\)  to lower mass, subhalos below \(10^8\,\rm M_\odot \) 
should be very or completely dark. N-body simulations indicate
that subhalos passing through the disk affect the kinematics of the
stars in the neighborhood out to several kpc, leaving waves that
persist for up to several hundred
Myr[2]}, [3]}. The proper motions measured
by Theia at a dozen locations, located just above and below the
galactic disk, should allow the first detection of kinematic
imprints for several dark subhalos[3]}, which
would be a major breakthrough.

Test the collisionless nature of Dark Matter.
Cosmological simulations of DM particles indicate that structures
(halos) have steep (“cuspy”) inner density
profiles[5]}. This has never been verified in
galaxies, whose intermittent outflows from supernovae explosions
and active galactic nuclei shake the inner gravitational potential
(where the gas dominates), causing violent relaxation that rapidly
leads the DM particles to settle to a more homogeneous inner
density profile[6]}. Dwarf spheroidal
galaxies (dSphs) around the Milky Way (except the three most
massive) are highly dominated by DM and should thus have cuspy
density profiles. Analysis of proper motions adds two dimensions to
the phase space probed by only using redshifts. Tests on mock data
shows that this dramatically improves the measure of the inner
slope of the density profile of dSphs[7]}, [3]}. If
Theia found cuspy inner density profiles in the targeted dSphs,
this would confirm that DM is collisionless. Conversely, if Theia found cores in the dSphs, this would provide the first measurement
on the cross-section of self-interaction, a major breakthrough in
particle physics.

Determine the shape of the outer halo of the Milky
Way. Cosmological simulations of cold DM
indicate[9]} that galaxy halos have prolate outer
shapes (while the stellar disks are oblate). Theia will measure
the proper motions of several distant known hyper-velocity stars
thought to have received huge velocity kicks in three-body
interactions involving the supermassive black hole at the center of
the Milky Way[10]}. These measurements combined with
redshifts should recover the 3D directions of the motion[3]} allowing
to determine the halo axis ratios to 5%, which is
beyond the scope of Gaia.

